Yes its safe to ship them together as long as you've got it locked in place and wrapped in the necessary anti-static protective wrap and enough padding. As far as shipping a desktop through the airline...every airport is different and every baggage handler is different. As you've seen on T.V probably..some just throw your luggage..others actually take pride in their job. If you're going to ship all separate components..just package it very carefully and perhaps OVER protect it.